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In particular, when thereis an alternating group A_5 action on a Spin 4-manifold X, we obtain: If X is smooth Spin4-manifold with non-positive signature and b_1=0, denote k=-σ/16 and m=b_2~+,then 2k+3≤m if b_2~++b_2~+≠2b_2~+(Z/A_5) and b_2~+≠0,where and are subgroups of A_5 generated by the elements s=∈A_5and t=∈A_5 respectively.

特别地，在Spin 4-流形具有非交换群A_5作用时，我们得到了：若X为光滑的具有非正符号差的Spin 4-流形，b_1=0，令k=-σ／16，m=b_2~+，如果X上具有Spin交错群A_5作用，且满足b_2~++b_2~+≠2b_2~+(X／A_5)，b_2~+≠0，则2k+3≤m，其中和分别为s=∈A_5和t=∈A_5生成的A_5的子群。

In chapter three, the dynamics of a driven spin-boson model is studied by means of the perturbation approach based on an unitary transformation. Analytical expressions for the population difference and the coherence of the two state system are obtained.

在第三章中，采用基于幺正变换的微扰方法，我们研究了驱动spin-boson模型的动力学，得到了在微波驱动下二能级系统的粒子数反转和相干性的解析表达式。

In this article,byJordan-Winger transformation,the weakly dimerized spin-1/2 anti-ferromagneticchain is transformed into quantum sine-Gordon model in the continuum limit.Onthe fundament of self-consistent field the usual field variable and canonical momen-tum are rescaled by using the Bogoliubov transformation.

我们利用Jordan-winger变换，在连续表象把量子二聚化spin-1/2反铁磁链哈密顿变换至sine-Gordon方程，在自洽场理论的框架内利用Bogoliubov变化重新标度了常规场变量和动量，有效地解决了远红外发散问题，自洽地得到了基态能和激发谱。

In Chapter 3, by using the technique of finite dimensional approximation of Seiberg-Wittentheory, the equivariant K-theory and some other methods, we study the problem of topologicalrestriction when there are smooth groups acting on Spin 4-manifolds such as the alternatinggroup A_5, cyclic group Z_6 and symmetric group S_3 with actions of odd type, consequently weimprove Furutas 10/8 theorem under the condition of group actions.

第三章运用Seiberg-Witten理论的有限维逼近技巧和等变K-理论等工具，研究了Spin 4-流形X上分别存在光滑交错群A_5、循环群Z_6和奇型三阶对称群S_3作用时，X的拓扑限制问题，在群作用下改进了Furuta的10／8定理。

The WGS 84 Datum is generally accepted as the best simple mathematical model for the overall shape of the earth, and is an ellipsoid with an equatorial radius of 6378.1370 km and a polar radius of 6356.7523 km, and is centred on the earth's centre and orientated to the spin axis.

WGS 84基准﹙ WGS 84 Datum ﹚被普遍接受为地球整体形状之最简单数学模型，是一个赤道半径﹙ equatorial radius ﹚ 6378.1370公里和北极半径﹙ polar radius ﹚ 6356.7523公里之椭球﹙ ellipsoid ﹚，以地球的中心为中心点，并定位於﹙ orientated to ﹚自转轴﹙ spin axis ﹚。

In chapter 2, the methods of spin dynamical simulation and fast Fourier transformation are introduced.

第二部分共有三章：第一章，我们简要地介绍该领域的一些背景和一些前人的工作；第二章，我们介绍自旋动力学模拟的方法和模拟计算中要用到的快速傅立叶变换方法；第三章，我们提出了两种有效钉扎Spin vortex的办法，一个是通过打孔的办法，另一个是通过小面积加垂直强磁场的办法。

The theme of the exhibition is "spin", which originates from the creative metaphor of the artist and the form of the artistic expression. In Chinese, spin actually means gyrate or convolution, which is usually adopted to describe the rotation of t he top and called as helix.

本次展览的主题是「spin」，这一主题源于艺术家的创作隐喻及艺术表达的形式，「spin」在中文字面上的意义具有「回旋」、「旋转」意思，通常用于形容陀螺的自转，又称螺旋。

We theoretically study the spin-polarized electron transport properties for quantum waveguide systems with attached stubs in the presence of Rashba spin-orbit coupling by the lattice Green function approach.

理论上研究了含stubs的Rashba自旋轨道耦合(spin-orbit coupling，简记SOC)量子波导系统的自旋极化输运性质。

The retest reliability, internal consistency reliability,discriminant validity and construct validity of the SPIN is satisfying. The SPIN deserves further emending and popularization.

SPIN具有良好的重测信度、内部一致性信度、区分效度和结构效度，值得进一步修订和推广。

The spin-1/2 dimerized antiferromagnetic system is related to spin-Peierls tran-sition.There are still some discrepancy on the behavior of the ground energy densityand energy gap,such as pure power-law,logarithmic correction to the pure power-law in the uniform,integer powers in the dimerized limit,etc.

自旋S-1/2的二聚化反铁磁链与spin-Peierls相变有关，在对其基态能和激发能隙的临界行为描述上仍存在一些不完全一致的观点：如均匀极限的纯幂级数律，纯幂级数律的对数修正；二聚化极限的整数幂级数行为等。

It goes back to what I told you...

现在回到我告诉过你的。。。

With a supporter in Mr Charest and an admirer in Mr Dumont, Mr Harper may be encouraged to call an election himself.

由于在沙雷那边有个支持者，杜蒙那边有个崇拜者，鼓励哈珀为自己举行一次选举。